I came across this article which I found very interesting, the emphasises are my own --
Abstract from 'Multiple nutritional factors and thyroid disease, with particular reference to autoimmune thyroid disease', by Margaret P Rayman --
"It is important to recognise that low iron stores may contribute to symptom persistence in patients treated for hypothyroidism in 5–10 % of whom symptoms remain despite being treated with levothyroxine (L-T4). An example is afforded by a small study in twenty-five Finnish women with persistent symptoms of hypothyroidism, despite appropriate L-T4 therapy, who became symptom-free when treated with oral iron supplements for 6–12 months. None of the women had anaemia or erythrocyte indices outside the reference range although all had serum ferritin <60 µg/l. Restoration of serum ferritin above 100 µg/l ameliorated the symptoms in two-thirds of the women. At least 30–50 % of hypothyroid patients with persisting symptoms despite adequate L-T4 therapy may, in fact, have covert Iron Deficiency." -
Note the levels here are significantly above what GPs consider to be "low". [The NHS say 25! I had ferritin level of 14 a year or so ago and my GP was not all that concerned!!!]
I also find it interesting that two thirds of those women who did not respond to T4 got symptom relief when they got ferritin over 100 ug/l due to (presumably) better T4 to T3 conversion, other healing of the thyroid and adrenals, and/or their hypo symptoms were actually covert iron deficiency.
I have also read that ferritin brings down RT3 (reverse T3) levels which again links into this as to why T4 didn't work until ferritin was raised.